111 research outputs found
Multivariate Shortfall Risk Allocation and Systemic Risk
The ongoing concern about systemic risk since the outburst of the global
financial crisis has highlighted the need for risk measures at the level of
sets of interconnected financial components, such as portfolios, institutions
or members of clearing houses. The two main issues in systemic risk measurement
are the computation of an overall reserve level and its allocation to the
different components according to their systemic relevance. We develop here a
pragmatic approach to systemic risk measurement and allocation based on
multivariate shortfall risk measures, where acceptable allocations are first
computed and then aggregated so as to minimize costs. We analyze the
sensitivity of the risk allocations to various factors and highlight its
relevance as an indicator of systemic risk. In particular, we study the
interplay between the loss function and the dependence structure of the
components. Moreover, we address the computational aspects of risk allocation.
Finally, we apply this methodology to the allocation of the default fund of a
CCP on real data.Comment: Code, results and figures can also be consulted at
https://github.com/yarmenti/MSR
Applying d-XChoquet integrals in classification problems
Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.Supported by Navarra de Servicios y TecnologĂas, S.A. (NASERTIC),
CNPq (301618/2019-4, 305805/2021-5), FAPERGS (19/2551-0001660-3), the
Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-
108392GB I00 (MCIN/AEI/10.13039/501100011033)
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